30 Philosophers, Chapter 6, Buddhism, Touchstone 15: Illusion: Self and Non-self. 

The terms Atman and Anatman relate to the idea of Self and the Buddhist doctrine of Non-Self. To understand non-self, understand emptiness as the idea that nothing exists permanently.

Self is expressed in Eastern thought as Atman, the true deeper soul. Your surface self changes, but Atman is the enduring reality within. Your soul. In some schools, like Advaita Vedanta, Atman is ultimately connected to Brahman, the deepest reality of all. This is where Buddhism turns.

Non-Self is the Buddhist insight of Anatman. Buddhism does not deny that you exist. You are still here, thinking, loving, and suffering. But it challenges the deeper claim of a permanent I. In Buddhism, the flame of life is real, but always changing.

Atman and Anatman, Self and Non-Self, work together. In Buddhism, the mistake is that we grip the self as permanent. We say this is me, this is mine, this is who I am, and then we suffer when life proves otherwise. The Buddhist path loosens that grip. It asks us to see that while the self is useful as a practical label, it is dangerous when mistaken for an eternal essence.

The TST twist is the idea that there is no value in to force one public answer for the unknownable. It does not ask everyone to choose the same answer about the eternal soul, Brahman, God, Heaven, or the final nature of consciousness. Those are deep worldview claims. But publicly, we still need common ground. We all share this material world during this life. TST asks us to build our public truths, public beliefs, and public systems on this material world during this life.